Evaluate
There are essentially two ways to approach this. The first is
The other is to use partial fractions:
Now, tanh^(-1) and ln have an overlapping domain and in this region everything is just fine and C = 0. The problem is that the ln solution has a much larger domain than the tanh one.
How can two solutions of an integral have different domains?
-Dan
I realize that much. My question is that I had thought the integral of an expression was unique up to an arbitrary constant. Because the domains are different, the tanh^(-1) and ln are different functions. I know of no reason why the tanh^(-1) solution does not also represent the most general solution.
-Dan